Image spatial transformation in DCT domain

In this paper, we report work on generalizing spatial relationships between the DCTs of any block and its sub-blocks, which paves the way for image processing in the JPEG compressed domain. The results reveal that DCT coefficients of any block can be directly obtained from the DCT coefficients of its sub-blocks and the inter-block relationship remains to be linear. Due to the fact that the corresponding coefficient matrix of linear combination is sparse, the computational complexity of the proposed algorithms is significantly lower than that of the existing methods.